Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.

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0
votes
2answers
95 views

Convert an expression from one form to another

I have this expression -0.433284-0.758719 x+0.00289158 x^2-0.443672 y+0.00149027 y^2 I want to express it in terms of $$\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}$$....
0
votes
1answer
75 views

strange result with trigonometric triple integral [duplicate]

I'm defining functions e[k_, t_] := Cos[Pi (k - 1) t] cosIntRaw[k_, l_, m_] := Integrate[e[k, t] e[l, t] e[m, t], {t, 0, 1}] cosInt[k_, l_, m_] := Assuming[Element[{k, l, m}, ...
1
vote
1answer
129 views

Unexpected result from FullSimplify

In the following simplification why doesn't Mathematica get a zero when asked to compute "Y-Z" eventually? ...
3
votes
1answer
55 views

Add rational linear expressions

I want to set work for my 17 year old calculus students and have access to Mathematica 7. I aim to create a worksheet with rational expressions which they will then decompose into partial fractions. ...
0
votes
1answer
416 views

How does Mathematica interpret a expression?

I'm a beginner to Mathematica. I'd read several document. But I still have a problem. For example, every expression in Mathematica are of the form ...
2
votes
2answers
219 views

Choosing a branch of the square root when performing a series expansion

I have the following problem. Consider expression f=Sqrt[(x-2y)^2] There is an obvious ambiguity in the definition of f ...
0
votes
2answers
378 views

Simplifying an expression containing radicals

Now I'm trying to use Mathematica to simplify an expression like this: $P \sqrt{-P + \sqrt{M^2 + P^2}} + \sqrt{(M^2 + P^2) (-P + \sqrt{M^2 + P^2})} - M \sqrt{P + \sqrt{M^2 + P^2}}$ where $P,M&...
0
votes
3answers
493 views

Why is 1. x (Times[1.`, x]) not simplified to x?

This is maybe a silly question, but I could not think of any logical reason why it is not simplified automatically. I was working with a big linear equation system with some constrained inequalities ...
0
votes
1answer
76 views

Inequality test returned unevaluated

I tried, Refine[Sin[k]^2/(k^2 + k + 1) < 1/(k^2), Element[k, Integers]] $\frac{\text{Sin}[k]^2}{1+k+k^2}<\frac{1}{k^2}$ It returns unevaluated. I ...
2
votes
2answers
315 views

Simplify results further

I have an extremely long result in polynomial form following some matrix operations. However, given the symmetry of the problem, I can safely say that the solution will reduce much further than is ...
0
votes
1answer
93 views

How to evaluate Floor[1/2 + Arg[z]/(2π)] with Re[z] > 0

I want to do a series expansion of an expression containing Gamma functions with specific arguments. An example is the following: ...
1
vote
1answer
134 views

How to obtain a useful answer from integration when Simplify is insufficient?

I have been trying to integrate a function AND get an output that is sufficiently simple as to be usable. Simply using the Simplify and ...
2
votes
2answers
695 views

Is it possible to simplify a trigonometric expression only in terms of $\cos (u)$ OR $\sin (u)$?

I want to expand the following expression into powers of $\cos(u)$ only: a1 + a2 Cos[2 u] + a3 Cos[4 u] + a4 Cos[6 u] The answer that I want (and which I found ...
2
votes
2answers
603 views

Rewriting one expression using a variable representing another expression [duplicate]

I have two expressions: w1 = (a+b)/c^2; w2 = (a^3 + 3 a^2 b + 3 a b^2 + b^3)/c^6; How can I ask Mathematica to try to find an alternative expression for ...
1
vote
1answer
1k views

Simplify square roots

If I simplify an equation like Sqrt[A^5]+5*Sqrt[A^3]-Sqrt[A] then I get (A^2+5A-1)*Sqrt[A] with no problems. But when I need to simplify Sqrt[(A^5) (1 + a) ] + 5 Sqrt[A^3 (1 + a)] - Sqrt[A (1 + a)] as ...
2
votes
2answers
197 views

Why Doesn't Mathematica Simplify Combinations of Quotients? (Integer Division)

I stumbled across this as part of a more complicated formula but it can be shown very simply: ...
0
votes
2answers
96 views

Place symbols from small to big

I am wondering how to compare the different values of ω I derived in this code, and place them in order as follows. (use Print ...
3
votes
1answer
206 views

Strange behavior of Reduce with a cubic equation

This equation: $(\frac{-a}{x})^2=\sqrt{\frac{1}{x}}$ at $a > 0$ and $x > 0$ has a clear solution $x=a^{4/3}$, doesn't it? However, ...
5
votes
2answers
177 views

FullSimplify inconsistent

I'm having problems using FullSimplify to simplify a differential equation. The expression is simplifying just as I would like when I express a variable ...
1
vote
1answer
134 views

Simplification of linear algebra [duplicate]

I have a few vectors defined as V1 = Array[v1,3] V2 = Array[v2,3] V3 = Array[v3,3] And I am trying to solve a very simple equation along the lines of ...
1
vote
1answer
196 views

How to simplify an expression into the sum of small fractions

I'm trying to simplify the following expression $$\frac{n.r \ p.q - (n.p + n.q) (p.r + q.r)}{(n.p + n.q)\ p.q}\to \frac{n.r}{n.p+p.q}-\frac{p.r+q.r}{p.q}$$ When I put it into Mathematica and use <...
1
vote
3answers
104 views

FullSimplify assumptions for function body

I'd like to pass an assumption to FullSimplify so whenever it gets a function that is squared and square rooted would return me only the function body, without <...
1
vote
1answer
199 views

Working with means and variances

My goal is to work out on the following equation: $$Mean(P)(1-Mean (P))\left (h + (1 - 2 h) (1 - \frac {Var (P)} {Mean (P) (1 - Mean (P))}) (1 - Mean (P)) + \frac {Var (P)} {Mean (P) (1 - Mean ...
1
vote
1answer
414 views

Factor vector out of a matrix

I am wondering how to factor a[1],a[2],...,a[4] out of sim so that I can write sim as the ...
2
votes
1answer
262 views

Taylor expansion of function of vectors—simplifying the output

I've got a real-valued function of several vectors $f(u,v,w)$ formed by taking scalar products of linear combinations of the vectors, I want to Taylor expand around small $v$ by writing $$f(u,\delta ...
3
votes
1answer
143 views

Do not understand expression returned by FullSimplify

Why Mathematica returns (sec x)^2? (Tan[x]^2 + 1 - Sec[x]^2)/(Sin[x]^2 + Cos[x]^2 - 1) // FullSimplify Sec[x]^2 Because ...
1
vote
0answers
45 views

Finding simpler implied formulas while preserving contradiction

I have two Presburger formulas A and B such that A∧B≡False. From these I need to find "simpler" formula A′ (as simple as I can make it) such that A→A′ and A′∧B≡False. Is there any simple way to ...
7
votes
3answers
350 views

Simplify with Assumptions Sqrt[(expr)^2]

While trying to simplify expressions in the form Sqrt[(expr)^2] when expr>0 I noticed a peculiar behavior that was not ...
1
vote
1answer
205 views

How to choose a solution of a differential equation?

I am trying to solve the following differential equation: ...
1
vote
1answer
360 views

Simplifying fractions

What ComplexityFunction (or other technique) can I use to have Mathematica pull things out of fractions? I have a rational function of several variables and I'd ...
0
votes
1answer
429 views

How to simplify power series in terms of functions

For example, after some computations mathematica outputs $$ \sum_{k=0}^{\infty} \frac{k g_k z^{k+4}}{(1-z)^3} $$ and we assume that $$G(z)= \sum_{k=0}^{\infty} g_k z^k $$ so the question is: how ...
0
votes
1answer
98 views

TeXForm without simplification

I'd like to be able to feed an expression into Mathematica, and have Mathematica convert that expression to TeXForm WITHOUT ANY SIMPLIFICATION WHATSOEVER. As a trivial example, currently, if I enter ...
2
votes
1answer
710 views

Truncate High order terms

Suppose I want to compute this : Series[Sin[1/f], {f, Infinity, 10}] but finally I prefer Sin[1/f] up to the fourth order in <...
1
vote
1answer
59 views

Substituting a function in the output

I have to calculate the derivatives of the function K defined in the code: ...
10
votes
3answers
1k views

Simplifying trig expressions containing Sqrt or Abs

The following Maple code can simplify abs(sin(x)) into -sin(x) given the condition ...
5
votes
0answers
163 views

How to get mathematica to simplify a result

I have the following output $\text{Li}_2\left(3-2 \sqrt{2}\right)-4 \text{Li}_2\left(-1+\sqrt{2}\right)$. This turns out to be equivalent to $\displaystyle\log^2(1+\sqrt{2})-\frac{\pi^2}{4}$. How ...
4
votes
2answers
195 views

Mathematica not recognising closed forms as specific values

I have a Mathematica program that outputs a piecewise function, and some parts of the expression are not being recognised as specific numbers when using FullSimplify...
1
vote
1answer
314 views

Get Cos[2 x] in “Solve”

My goal is to get an analytical solution of x ( $\lambda$ in the problem), when $\epsilon$ (f[x] in the problem) is maximum (use inverse form). I found that if I can use trigonometric identity to ...
1
vote
1answer
78 views

Solve never terminates with simultaneous equation set

I have the following set of simultaneous equations that I want to solve symbolically. The two unknowns are $a$ and $d$. $a=\frac{c*(d/10)}{1 + (f/130) + (d/50)} - \frac{a}{1 + (a/100) + (d/100) + (f/...
0
votes
0answers
54 views

Always the same problem with Conjugate [duplicate]

I want to compute something like : ...
2
votes
4answers
193 views

Cancelling units in two-argument ArcTan

Consider ArcTan[3, -3] (* out: *) -Pi/4 ArcTan[3 a Sin[t/2], -3 a Sin[t/2]] (* out: *) ArcTan[3 a Sin[t/2], -3 a Sin[t/2]] However, we can fix the ...
7
votes
3answers
651 views

Problems using hand-made transformation functions

I experience difficulties when using custom transformation rules. Below I give two concrete problems. I am interested in fixing each of them and in understanding what is wrong with my attitude to the ...
0
votes
1answer
80 views

How to simplify or improve my code (or how to Flatten inside the matrix)?

I believe that it may be simplified, but I have no ideas anymore.. I need to flatten inside each element of array. F.ex. {{1}, 128552, 6, 1} ---> {1, 128552, 6, 1} Input data (Z - requests, t - ...
0
votes
1answer
252 views

Impose an specific Trigonometric expansion with TrigExpand

Is there a way to impose in mathematica an specific trigonometric expansion with TrigExpand? I have various double-angle expressions for cosine and sine in my ...
3
votes
1answer
114 views

How to make Mathematica Simplify?

Let us define r1 = 1;r2 = 2; and ...
1
vote
2answers
622 views

How can I separate two parts of power of Exponential functions?

How can I separate two parts of power of exponential functions in Mathematica? I have an expression similar to this one: a*b*Exp[u+v]+c*Exp[u] I want to set <...
4
votes
2answers
1k views

Mathematica won't simplify the expression with obvious common factor of a fraction

I have an expression obtain from an integral, which is: Integrate[ϵ^2/Sqrt[(ϵ - u)^2 + Δ^2], ϵ] // FullSimplify The denominator and numerator of the result have ...
1
vote
1answer
510 views

Factor a Vector

Does there exist a function in Mathematica that simply takes out a common factor from a vector/list of expressions? This seems like such a simple operation that I am surprised that I could not find it ...
0
votes
1answer
105 views

Decompose Expression into Segments

Say I have an expression test = 3 x1^2 - 2 x3^-3 and I would like to decompose the expression into {3 x1^2, -(2/x3^3)}, I can do ...
0
votes
1answer
75 views

Resolve a conditional expression including exists and forall

I don't know the Resolve function exactly, especially when involved with Exists and ForAll, ...